The award was funded by the Technical University of Delft in the honor of Warner T. Koiter, who was a professor at the university from 1949 till 1979. Koiter's most influential work dealt with the non-linear stability of structures.

The recipient is given an honorarium and a bronze plaque.

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The Koiter Medal Committee consists of the five recent Koiter Medalists, the five members of the executive committee of the ASME International Applied Mechanics Division (AMD), and the five recent past chairs of the AMD. Upon receiving recommendations from the international community of applied mechanics, the Committee nominates a single medalist every year. This nomination is subsequently approved by the ASME; no case has been reported that the ASME has ever overruled a nomination of the Koiter Medal Committee. See the list of current members of the Committee.